An effective medium modeling technique is proposed to homogenize the periodic objects embedded in layered media. The homogenization is based on the same scattering coefficients. An integral equation based approach is adopted to solve the scattering problem of original structures. Our modeling results are compared with Maxwell-Garnett mixing formula and published results. Good agreements have been observed. Periodic metal patches embedding in layered dielectric structure is fabricated and measured to validate the modeling technique. The difference between experiment results and proposed modeling results is less than 3%.
2. Njoku, C. C., W. G. Whittow, and J. C. Vardaxoglow, "Simulation methodology for synthesis of antenna substrates with microscale inclusions," IEEE Trans. Antennas Propag., Vol. 60, No. 5, 2194-2202, 2012.
3. Merrill, W. M., R. E. Diaz, M. M. Lore, M. C. Squires, and N. G. Alexopoulos, "Effective medium theory for artificial materials composed of multiple sizes of spherical inclusions in a host continuum," IEEE Trans. Antennas Propag., Vol. 47, No. 1, 142-148, 1999.
4. Zheng, G., B.-Z. Wang, H. Li, X.-F. Liu, and S. Ding, "Analysis of finite periodic dielectric gratings by the finite-difference frequency-domain method with the sub-entire-domain basis functions and wavelets," Progress In Electromagnetics Research, Vol. 99, 453-463, 2009.
5. Lerisirimit, C. and D. Torrungrueng, "Fast capacitance extraction for finite planar periodic structures using the generalized forward-backward and novel spectral acceleration method," Progress In Electromagnetics Research, Vol. 96, 251-266, 2009.
6. Hu, F. and J. Song, "Integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 848-856, 2010.
7. Zhao, T., J. Song, and T. Kamgaing, "Modeling and experimental test of effective dielectric constant of multilayer substrate with periodic metal inclusion," IEEE MTT-S International Microwave Symposium, 1-3, Jun. 2013.
8. Smith, D. R., S. Schultz, P. Marko, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phy. Rev. B, Vol. 65, 016608, 2004.
9. Zhao, T., J. Song, T. Kamgaing, and Y. S. Mekonnen, "An efficient modeling approach for multilayered dielectric embedded with periodic metal," Microwave and Optical Technology Letters, Vol. 56, No. 6, 1387-1391, 2014.
10. Wu, F. and K. W. Whites, "Quasi-static effective permittivity of periodic composites containing complex shaped dielectric particles," IEEE Trans. Antennas Propag., Vol. 49, No. 8, 1174-1181, 2001.
11. Das, N. K., S. M. Voda, and D. M. Pozar, "Two methods for the measurement of substrate dielectric constant," IEEE Trans. Microwave Theory and Tech., Vol. 35, No. 7, 636-642, 1987.
12. Mondal, J. P. and T.-H. Chen, "Propagation constant determination in microwave fixture de-embedding procedure," IEEE Trans. Microwave Theory and Tech., Vol. 36, No. 4, 706-714, 1988.
13. Balanis, C. A., Advanced Engineering Electromagnetic, J. Wiley & Sons, New York, 1989.